Imported .obj just showing a black texture
You need to create a material. Blender has two different renderers, Blender internal (the old) and Cycles (the new and nowadays standard). Materials are different in these two. I suggest you pick cycles.

First, make sure you are using cycles. You find the menu in the top bar of blender.



Now, select the object and go to the Material tab. A material should be selected for the object. If it not, create it:



If the material was created for Blender Internal, you may have to press "use nodes". Now, your material is ready to accept a texture map. Press the little button with a dot to the far right of the "Color" field. In the menu that pops up, select "Image Texture".



Now hit open and browse to your texture. You have now created a material with a diffuse shader and an image texture. It should look like this:



If it doesn't show up on the model, it means your UV-mapping on the model is wrong (probably). Since the texture only works for a specific UV-mapping, you must get this right when you import.

The next step if you intend to render this is to work on the shader some more. You do this in the node editor. Your shader will look like this: